Chromatic dispersion equalizer adaption systems and methods

ABSTRACT

Described herein are systems and methods that perform coarse chromatic dispersion (CD) compensation by applying precomputed coarse front-end equalizer (FEE) tap weights to a receiver based on an assumed propagation distance. After a waiting period, the FEE tap weights are applied, and it is determined whether the FEE tap weights cause a decision-directed tracking of channel rotations to satisfy a stability metric. In response to the stability metric not being satisfied, the assumed propagation distance is adjusted and used to obtain updated FEE tap weights. Conversely, if the stability metric is satisfied, a fine CD compensation is performed that comprises maintaining the updated FEE tap weights; performing an iterative least-mean-squared (LMS) error adaption to adjust Back-End Equalizer (BEE) tap weights and obtain updated BEE tap weights; and using the updated BEE tap weights to adjust the FEE tap weights to, ultimately, have the BEE output an equalized data bit stream.

CROSS REFERENCE TO RELATED PATENT APPLICATIONS

This application is related to and claims priority benefit under 35U.S.C. § 120 to co-pending and commonly-assigned U.S. patent applicationSer. No. 17/023,147, entitled “Chromatic Dispersion Equalizer AdaptionSystems and Methods,” filed on Sep. 16, 2020, now U.S. Pat. No.11,231,184, and listing as inventor Charles Razzell, which patentapplication claims priority benefit under 35 U.S.C. § 119(e) from U.S.Provisional Patent Application, Ser. No. 62/942,045 entitled “ChromaticDispersion Equalizer Adaption Systems and Methods,” filed on Nov. 29,2019 and listing as inventor Charles Razzell. Each reference mentionedin this patent document is incorporated by reference herein in itsentirety and for all purposes.

BACKGROUND

The present disclosure relates generally to signal processing inhigh-speed telecommunication circuits. More particularly, the presentinvention relates to systems and methods that perform CD compensation indual-polarization coherent optical transmission and similarapplications. In the past few decades, telecommunication networks haveseen an ever-increasing demand for bandwidth. Large available bandwidthis a major factor in the increasing popularity of high-speed opticalcommunication systems—whether for transferring data from chip to chip orbetween Wide Area Network (WAN) fiber-optic links. For example, opticaltransceivers designed for short-distance (e.g., a few hundred meters)interconnects over optical fiber are in high demand in data center andcampus networks. However, the presence of chromatic dispersion (CD) andother transmission impairments limit the rate at which data can betransported in an optical communication channel. Accordingly, it wouldbe desirable to have low-complexity systems and methods that overcomethe shortcomings of existing designs and mitigate the effects ofchromatic dispersion, without the need for costly and complex signaldigitization using DSPs.

BRIEF DESCRIPTION OF THE DRAWINGS

References will be made to embodiments of the disclosure, examples ofwhich may be illustrated in the accompanying figures. These figures areintended to be illustrative, not limiting. Although the accompanyingdisclosure is generally described in the context of these embodiments,it should be understood that it is not intended to limit the scope ofthe disclosure to these particular embodiments. Items in the figures maybe not to scale.

FIG. 1 is a block diagram of a conventional dual polarization quaternaryamplitude modulation (DP-QAM) receiver architecture that is based onanalog signal processing.

FIG. 2 illustrates and exemplary chromatic dispersion equalizer systemaccording to embodiments of the present disclosure.

FIG. 3 illustrates and exemplary circuit implementation of a chromaticdispersion equalizer system according to embodiments of the presentdisclosure.

FIG. 4A and FIG. 4B show simulation results for constellation diagramsfor X- and Y polarization outputs for a prior art equalizer design.

FIG. 5A and FIG. 5B show improved simulation results for constellationdiagrams for X- and Y polarization outputs using a CD equalizer systemaccording to embodiments of the present disclosure.

FIG. 6 is a flowchart of an illustrative process for CD equalization,according to embodiments of the present disclosure.

FIG. 7 is a flowchart of another illustrative process for CDequalization, according to embodiments of the present disclosure.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the following description, for purposes of explanation, specificdetails are set forth in order to provide an understanding of thedisclosure. It will be apparent, however, to one skilled in the art thatthe disclosure can be practiced without these details. Furthermore, oneskilled in the art will recognize that embodiments of the presentdisclosure, described below, may be implemented in a variety of ways,such as a process, an apparatus, a system/device, or a method on atangible computer-readable medium.

Components, or modules, shown in diagrams are illustrative of exemplaryembodiments of the disclosure and are meant to avoid obscuring thedisclosure. It shall also be understood that throughout this discussionthat components may be described as separate functional units, which maycomprise sub-units, but those skilled in the art will recognize thatvarious components, or portions thereof, may be divided into separatecomponents or may be integrated together, including integrated within asingle system or component. It should be noted that functions oroperations discussed herein may be implemented as components. Componentsmay be implemented in software, hardware, or a combination thereof.

Furthermore, connections between components or systems within thefigures are not intended to be limited to direct connections. Rather,data between these components may be modified, re-formatted, orotherwise changed by intermediary components. Also, additional or fewerconnections may be used. It shall also be noted that the terms“coupled,” “connected,” or “communicatively coupled” shall be understoodto include direct connections, indirect connections through one or moreintermediary devices, and wireless connections.

Reference in the specification to “one embodiment,” “preferredembodiment,” “an embodiment,” or “embodiments” means that a particularfeature, structure, characteristic, or function described in connectionwith the embodiment is included in at least one embodiment of thedisclosure and may be in more than one embodiment. Also, the appearancesof the above-noted phrases in various places in the specification arenot necessarily all referring to the same embodiment or embodiments.

The use of certain terms in various places in the specification is forillustration and should not be construed as limiting. The terms“include,” “including,” “comprise,” and “comprising” shall be understoodto be open terms and any lists the follow are examples and not meant tobe limited to the listed items. All documents cited herein areincorporated by reference herein in their entirety. In this document theterm “tap weights” refers to weights, states, coefficients, or gains offilter taps.

Although embodiments described herein are given in the context ofoptical communication systems and methods, persons skilled in the artwill recognize that the teachings of the present disclosure are notlimited to optical communication applications and may equally be used inwired networks, satellite communication, and the like.

Coherent optical links communicate data over different communicationchannels that correspond to different phases and polarizations of aninput signal to the fiber. In a dual-polarization coherent opticaltransmission system, X- and Y-polarization channels carry ideallyindependent in-phase (I) and quadrature phases (Q) of the X- andY-polarizations, conventionally denoted as tributaries XI, XQ, YI andYQ—one for each branch—such that when level 4 pulse-amplitude modulation(4-PAM) is used, each branch yields two bits for every unit interval(UI), and the combination of all four branches yields a total of 8 bitsper UI.

FIG. 1 is a block diagram of a conventional DP-QAM receiver architecturethat is based on analog signal processing. Receiver 100 is a homodynereceiver driven by an on-channel laser (not shown) that acts as thelocal oscillator. The arrangement of the polarization beam splitter and90° hybrids 106 is designed to provide balanced quadrature light outputsfor each of the two orthogonal polarizations, conventionally labeled Xand Y, which are incident on eight photodiodes 108 that are arranged inbalanced pairs. This arrangement results in four bipolar photocurrents110 that are amplified by respective Trans Impedance Amplifiers (TIAs)112, corresponding to I and Q-phases of the X- and Y-polarizations,respectively. Thus, four branches of receiver 100, i.e., XI, XQ, YI, YQ,are available for further signal processing in the analog domain.

However, imperfections inherent to the transmitter, receiver 100, andoptical fiber introduce unwanted delays that cause polarization andphase in the four channels to arrive at the receiver with unknown phaserotation and phase polarization dimensions that the receiver cannotidentify from the recovered information.

For example, since the index of refraction of a fiber channel varies(typically decreasing for increasing wavelength in materials that do notabsorb light) with the frequency of the light due to material propertiesor geometry of the fiber that acts as an optical waveguide, CD andcorresponding group delay depend on the optical wavelengths propagatedin the form of short pulses of light. Given a signal with sufficientlybroad frequency bandwidth, depending on the medium and the wavelength,higher frequencies components of that signal will experience greatergroup delay than low-frequency components, such that higher frequencyspectral components undergo a different delay in the transmission mediumthan lower frequency components of the same sign. As an example, thegroup delay dispersion of silica is +36 fs²/mm at 800 nm and −22 fs²/mmat 1500 nm. Zero group delay dispersion is reached close to 1270 nm.Such temporal spreading of a pulse, which represents the information,significantly increases bit-error rate (BER), decreases the rate atwhich data can be transported in a channel, and leads to a reduction ofthe opening in the so-called eye-pattern. This dispersion effect worsenswith increasing length of the fiber, causing the BER to becomeunacceptable at lengths greater than a few km at 1550 nm and, thus,requiring electronic equalization to regenerate communication signals.

If CD were the only transmission impairment that is introduced,dispersion compensating fibers may be used. Alternatively, assuming thatthe type and length of the fiber are known, FEE tap weights could beinitialized to values that allow for proper compensation of group delayeffects caused by the fiber's characteristic.

In practice, however, determining suitable tap weights is rendereddifficult by the fact that in many applications the type and exactlength of the fiber that the system is connected to are not known apriori or are subject to change. This difficulty is exacerbated by thepresence of additional impairments, such as channel-induced inter-symbolinterference (ISI) that is caused by bandwidth limitations. Moreover, atthe input to receiver 100, all polarizations may be mixed into eachother, random phase orientations may exist, and there may be noreference point that would allow one to identify a valid signal. As aresult, an attempt to change or adjust tap weights cannot rely on localdecision-directed feedback for correction while an open-loop approach tocomputing the FEE coefficients is, on its own, unlikely to be sufficientto restore the signal integrity to an acceptable BER.

Therefore, it is desirable to have systems and methods that mitigate theeffects of CD and increase the tolerance against resulting errorswithout the need for Nyquist-rate DSPs for signal digitization andwithout requiring human intervention.

FIG. 2 illustrates and exemplary CD equalizer system according toembodiments of the present disclosure. System 200 comprises CD front-endequalizer (FEE) 202, LMS adaption circuit 210, back-end equalizer (BEE)220. A person of skill in the art will appreciate that a frequencycorrection circuit may be placed before LMS adaption circuit 210. Suchperson will further appreciate that part or all of system 200 may beimplemented as a single circuit. It is noted that FEE 202 typically hasno cooperation from the transmitter (not shown), which may be connectedto a random length fiber over which FEE 202 has no control. Embodimentsof the present disclosure allow for any length of fiber and fortransmitters to use any standard or proprietary protocol.

In operation, system 200 may perform CD equalization by using LMSadaption circuit 210 to perform an iterative LMS error adaption thatadjusts tap weights in BEE 220. In embodiments, the BEE tap weights maybe used to adjust tap weights in FEE 202. As a result, system 200outputs data bit stream 230 that has been equalized. Advantageously,system 200 provides for some amount of blind adaption of tap weights inFEE 202 to mitigate the effects of CD.

As is known from the patent applications mentioned herein andincorporated by reference, existing electronic polarization controlloops are useful for separating and phase-aligning dual polarizationcoherent signals. Least mean square (LMS) adaption is used in thecoherent optical signal processor to track random phase rotations andother impairments. LMS adaption is performed using a continuous versionof the classic RLMS update equation on eight coefficients held, forexample, in analog integrators as charge on capacitors.

Eight coefficients represent a 2×2 complex matrix that is used toseparate and phase correct the incoming analog signal:

$\begin{bmatrix}E_{XO} \\E_{YO}\end{bmatrix} = {\begin{bmatrix}C_{1X} & C_{1Y} \\C_{2X} & C_{2Y}\end{bmatrix} \cdot \begin{bmatrix}E_{XI} \\E_{YI}\end{bmatrix}}$

Considering a dual-polarization coherent optical receiver having fourindependent branches, XI, XQ, YI, and YQ, that represent the I and Qcomponents of two arbitrary orthogonal polarizations X and Y, andneglecting losses and dispersion in the optical channel, the observed Xand Y signals in the receiver branches may be represented in complexnotation as

${\begin{bmatrix}X_{in} \\Y_{in}\end{bmatrix} = {{{{e^{i{\psi/2}}\begin{bmatrix}e^{i\;{\phi_{1}/2}} & 0 \\0 & e^{{- i}\;{\phi_{1}/2}}\end{bmatrix}}\begin{bmatrix}{\cos\;\theta} & {\sin\;\theta} \\{{- s}{in}\;\theta} & {\cos\;\theta}\end{bmatrix}}\begin{bmatrix}e^{i\;{\phi_{0}/2}} & 0 \\0 & e^{{- i}\;{\phi_{0}/2}}\end{bmatrix}}\begin{bmatrix}E_{xi} \\E_{yi}\end{bmatrix}}},$

where ψ, ϕ1, θ and ϕ0 are four real parameters, ψ represents theabsolute phase, ϕ0 represents relative phase shift between X- andY-polarization signals before a plane polarization rotation by θ, and ϕ1represents the relative phase shift afterwards. By multiplying all ofthese sub-components, a single 2×2 complex matrix is obtained thatrelates the received signal to the transmitted signal as follows:

${\begin{bmatrix}X_{in} \\Y_{in}\end{bmatrix} = {\begin{bmatrix}\Gamma_{1X} & \Gamma_{1Y} \\\Gamma_{2X} & \Gamma_{2Y}\end{bmatrix}\begin{bmatrix}E_{xi} \\E_{yi}\end{bmatrix}}},$

The matrix Γ is unitary due to the factors that used to create it.Matrix Γ is therefore invertible, and an estimate of the originaltransmitted waveforms may be obtained as:

$\begin{bmatrix}{\hat{E}}_{xi} \\{\hat{E}}_{yi}\end{bmatrix} = {{\begin{bmatrix}\Gamma_{1X} & \Gamma_{1Y} \\\Gamma_{2X} & \Gamma_{2Y}\end{bmatrix}^{- 1}\begin{bmatrix}X_{in} \\y_{in}\end{bmatrix}}.}$

Thus, there exists a new demixing matrix, C

Γ⁻¹, which may be substituted into the above matrix equation to yield:

$\begin{bmatrix}X_{out} \\Y_{out}\end{bmatrix}\overset{def}{=}{\begin{bmatrix}{\hat{E}}_{xi} \\{\hat{E}}_{yi}\end{bmatrix} = {{\begin{bmatrix}C_{1X} & C_{1Y} \\C_{2X} & C_{2Y}\end{bmatrix}\begin{bmatrix}X_{in} \\Y_{in}\end{bmatrix}}.}}$

This represents two linear equations, each having two complexcoefficients, i.e.,

X_(out) = C_(1X)X_(in) + C_(1Y)Y_(in) andY_(out) = C_(2X)X_(in) + C_(2Y)Y_(in).

Although these two equations look independent, they derive from onlyfour independent real parameters and, hence, the coefficients on the topand bottom rows of the matrix are not independent from each other.Nevertheless, they may be treated as independent for the purposes ofiterating towards a solution as long as they do not converge in a mannersuch that the top and bottom rows are related to each other by aproportionality constant, i.e., X_(out)=αY_(out), where a is theproportionality constant.

Solving one of these equations (and assuming that a similar techniquemay be applied to the other similar equation) providesX_(out)=C_(1X)X_(in)+C_(1Y)Y_(in), in which only the observed signalsX_(in) and Y_(in) are known. Although the estimated symbolÊ_(xi)=X_(out) is unknown, it is known that ideal samples of X_(out)should be drawn from the finite alphabet of the modulation constellationin use, e.g., in 16-QAM modulation, which can be considered as 4-PAMsignaling in each of the quadrature channels. Hence, for any candidatetrial values of C_(1X) and C_(1Y), the error may be estimated as thedifference between the nearest valid constellation point and the outputsignal X_(out), denoted by Q (X_(out)) and X_(out). Let e(X_(out))

Q X_(our))−X_(out). The quantizer, Q, may be defined as two 4-PAMmodulation quantizers that operate, at least approximately,independently in the I- and Q-dimensions.

Based on the known complex LMS update equation, one may iterate towardsa minimum error condition by accumulating into coefficients C_(1X) andC_(1Y) using the following update equations:

C_(1X) ⇐ C_(1X) + μ(Q(X_(out)) − X_(out)) ⋅ X_(in)^(*)C_(1Y) ⇐ C_(1Y) + μ(Q(X_(out)) − X_(out)) ⋅ Y_(in)^(*)X_(out) = X_(i n) ⋅ C_(1X) + Y_(i n)C_(1Y)

Expanding the above complex expressions using:

${X_{out}\overset{def}{=}{X_{Iout} + {iX}_{Qout}}};{C_{1X}\overset{def}{=}{C_{1{XI}} + {iC}_{1{XQ}}}};{C_{1Y}\overset{def}{=}{C_{1{YI}} + {iC}_{1{YQ}}}};$${C_{2X}\overset{def}{=}{C_{2{XI}} + {iC}_{2{XQ}}}};{C_{2Y}\overset{def}{=}{C_{2{YI}} + {iC}_{2{YQ}}}}$

yields for computation of the output for real and imaginary parts of theX-polarization output:

X_(Iout) = X_(I_(i n)) ⋅ C_(1XI) − X_(Q i n) ⋅ C_(1XQ) + Y_(I_(i n)) ⋅ C_(1YI) − Y_(Qin) ⋅ C_(1YQ)X_(Qout) = X_(Qin) ⋅ C_(1XI) + X_(I_(i n)) ⋅ C_(1XQ) + Y_(Qin) ⋅ C_(1YI) + Y_(I_(i n )) ⋅ C_(1YQ).

The coefficient update equations for the real and imaginary parts ofupper row of the coefficient matrix are then:

C_(1XI) ⇐ C_(1XI) + μ(Q(X_(Iout)) − X_(Iout)) ⋅ X_(I_(i n)) + μ(Q(X_(Qout)) − X_(Qout)) ⋅ X_(Q_(i n))C_(1XQ) ⇐ C_(1XQ) + μ(Q(X_(Qout)) − X_(Qout)) ⋅ X_(I_(i n)) − μ(Q(X_(Iout)) − X_(Iout)) ⋅ X_(Q_(i n))C_(1YI) ⇐ C_(1YI) + μ(Q(X_(Iout)) − X_(Iout)) ⋅ Y_(I_(i n)) + μ(Q(X_(Qout)) − X_(Qout)) ⋅ Y_(Q_(i n))C_(1YQ) ⇐ C_(1YQ) + μ(Q(X_(Qout)) − X_(Qout)) ⋅ Y_(I_(i n)) − μ(Q(X_(Iout)) − X_(Iout)) ⋅ Y_(Q_(i n))

Similarly, one may write for the Y-polarization output:

Y_(out) = X_(in) ⋅ C_(2X) + Y_(in)C_(2Y),

which expands to:

Y_(Iout) = X_(I_(i n)) ⋅ C_(2XI) − X_(Q i n) ⋅ C_(2XQ) + Y_(I_(i n)) ⋅ C_(2YI) − Y_(Qin) ⋅ C_(2YQ)X_(Qout) = X_(Qin) ⋅ C_(2XI) + X_(I_(i n)) ⋅ C_(2XQ) + Y_(Qin) ⋅ C_(2YI) + Y_(I_(i n )) ⋅ C_(2YQ).

And the corresponding update equations are:

C_(2X) ⇐ C_(2X) + μ(Q(Y_(out)) − Y_(out)) ⋅ X_(in)^(*)C_(2Y) ⇐ C_(2Y) + μ(Q(Y_(out)) − Y_(out)) ⋅ Y_(i n)^(*)

which expand to:

C_(2XI) ⇐ C_(2XI) + μ(Q(Y_(Iout)) − Y_(Iout)) ⋅ X_(I_(i n)) + μ(Q(Y_(Qout)) − Y_(Qout)) ⋅ X_(Q_(i n))C_(2XQ) ⇐ C_(2XQ) + μ(Q(Y_(Qout)) − Y_(Qout)) ⋅ X_(I_(i n)) − μ(Q(Y_(Iout)) − Y_(Iout)) ⋅ X_(Q_(i n))C_(2YI) ⇐ C_(2YI) + μ(Q(Y_(Iout)) − Y_(Iout)) ⋅ Y_(I_(i n)) + μ(Q(Y_(Qout)) − Y_(Qout)) ⋅ Y_(Q_(i n))C_(2YQ) ⇐ C_(2YQ) + μ(Q(Y_(Qout)) − Y_(Qout)) ⋅ Y_(I_(i n)) − μ(Q(Y_(Iout)) − Y_(Iout)) ⋅ Y_(Q_(i n))

The result is eight real-valued update equations that may be used tofind the four complex coefficients of the demixing matrix. Inembodiments of the present disclosure, these update equations may beimplemented in the analog domain as continuous-time integrators.

In embodiments, 16-QAM or NRZ error detection is used in a feedback loopto track the complex coefficients of the 2×2 Jones matrix. Inembodiments, to set suitable initial positive or negative tap weightsthat enable tracking and allow decisions, such as distinguishing the 16points in a constellation, to be performed with confidence, LMS adaptioncircuit 210 may use a circuit, such as unitary forcer circuit disclosedin and U.S. Patent Application No. 62/931,122, filed on Nov. 5, 2019,entitled “ANALOG COHERENT SIGNAL PROCESSING SYSTEMS AND METHODS,”listing as inventors Charles Razzell and Edem Ibragimov, and U.S. PatentApplication No. 62/931,127, filed on Nov. 5, 2019, entitled “DYNAMICERROR QUANTIZER TUNING SYSTEMS AND METHODS,” listing as inventorsCharles Razzell, which applications are herein incorporated by referenceas to their entire contents.

As mentioned therein, the unitary forcer may be used to estimate thenumerator and denominator (or metrics associated therewith) of acorrelation coefficient that represents a correlation between the firstand the second row vectors of a coefficient matrix, e.g., an LMS-adaptedinverse Jones matrix. In embodiments, the numerator exceeding by apredetermined amount a metric that represents the denominator may berepresentative of a correlation that is indicative of a predeterminedfraction being exceeded. Such metric may comprise a product ofanti-diagonal elements that exceed a product of main diagonal elementsassociated with the coefficient matrix. Excessive correlation indicatesa possible misconvergence and is used to trigger a reset to an LMSalgorithm.

In embodiments, a metric that represents a relatively low correlationbetween two rows of the Jones matrix may be used as a stability metricthat reflects the current quality of the tracking of the polarizationand carrier phase angles, which in turn depends on the success of thecurrently-chosen set of FEE tap weights to make the individualconstellation points distinguishable. BEE 220 may be used to furtherequalize incoming signals, such that the ISI of the final output signalfrom the receiver is improved before being fed to a subsequent clock anddata recovery circuit (CDR, not shown). Advantageously, conventionaldecision-directed error detection may then be used to drive the feedbackloops since the carrier phase is already corrected by LMS block 210. Asthe LMS loop continuously adapts, BEE 220, in effect, overcomes ashortcoming caused by FEE 202 which has a limited number of taps. Inembodiments, the residual ISI at the input to BEE 220 obtained in termsof the tap weights that arise in BEE 220 may, thus, be used to determinehow to adjust FEE 202, as discussed in greater detail with reference toFIG. 3.

FIG. 3 illustrates and exemplary circuit implementation of a CDequalizer system according to embodiments of the present disclosure. CDequalizer system 300 comprises CD FEE 202, carrier frequency offset(CFO) 320, polarization and carrier phase correction circuit 330, BEE220, and digitally controlled oscillator (DCO) 350.

In embodiments, receiver input 302 receives four uncorrected electricalsignals 304 that may comprise of a mixture of X- and Y-polarizationsrepresenting respective receiver branches XI, XQ, YI, and YQ. Signals304 may output by differential TIAs that, similar to FIG. 1, monitorfour pairs of photodiodes (not shown). FEE 320 may be used to reduce oreliminate CD, ISI, and receiver skew. It is understood that FEE 320 maybe implemented as a number of analog FEEs, e.g., one for X-polarizationand one for Y-polarization, that utilize tap weights chosen such as tocause the down-stream receiver feedback loops to lock correctly.Receiver input 302 may be passed to four analog FIR filters within FEE202 that each may have the same structure and comprise a number of timedelays, e.g., implemented as on-chip transmission lines.

In embodiments, coarse values for the tap weights for FEE 202 may bestored in memory as corresponding entries in a look-up table that mayspecify a set of suitable, e.g., precomputed, FIR coefficients for anassumed propagation distance discussed further below. In embodiments,four independently determined coefficient vectors may be used.

In embodiments, FEE 202 is implemented as a T/2-spaced FEE. However,this is not intended as a limitation on the scope of the presentdisclosure as any different spacing may be selected. As a person ofskill in the art will appreciate, if. If the taps in FEE 292 are tooclosely spaced in the time, hardware resources such as multiplier andadders are wasted. Therefore, the spacing should be chosen such as toprovide sufficient, but not excessive, resolution in the frequencyresponse.

Polarization and carrier phase correction circuit 330 may comprise errorslicers, adaption circuits, complex multipliers, and supervisory controlcircuitry. Circuit 330 may be viewed as four complex multipliers thatare representative of the Jones matrix. The multipliers multiply atime-varying 2×2 complex matrix by four input signals (e.g., 304) thateach may be viewed as two complex signals, where the complex tap weightsmay be continuously adapted by using the LMS update equation, or anyother weight updating method such as RLS, to correct for thepolarization and phase rotations in the optical channel.

In embodiments, adaption of the complex coefficients of the 2×2 Jonesmatrix may be implemented by one analog LMS loop, e.g., within circuit330, for each coefficient. In embodiments, to correct for polarizationand phase changes in the fiber, four real error slicers may monitor andcompare the error, which may be a time-varying signal, to an idealconstellation and, based on the comparison, drive four complex adaptioncircuits that determine four complex coefficients for the Jones matrix.

In embodiments, CFO 330 correction multiplies respective X- andY-branches with a complex local oscillator signal provided on sin 374and cos 374 input ports. In embodiments, BEE 350 may use a 4-PAMdecision-based error signal (or 16-QAM if considered two-dimensionally)to train an iterative analog complex LMS with, e.g., five complex taps.BEE 350 performs residual ISI correction iteratively performing agradient search that selects tap weights such as to minimize the meansquared error between the output signal and an ideal set of modulationconstellation values. This has the beneficial effect of inversefiltering the low-pass filtering effect caused by amplifier parasiticsalong with any other sources of residual ISI (e.g., incompleteequalization in the FEE). A gain block in the error feedback loop (notshown) may be used to adjust the speed of adaption. The output of BEE350 comprises corrected 4-PAM signals that may be fed into a CDR anddecision slicer (not shown) to obtain desired symbols.

In embodiments, system 300 performs CD equalization by applying to FEE202 control parameters, such as tap weights that have been precomputedby using an assumed propagation distance, to provide a coarse CDcompensation. In embodiments, e.g., after waiting a predetermined periodof time, it may be determined whether the tap weights, as, a performancemeasure, have caused a decision-directed tracking of channel phase andpolarization rotations to satisfy the stability metric discussed withreference to FIG. 2. As a person of skill will appreciate, circuit 300should track and, thus, provide a stable frame of reference to BEE 220before BEE 220 is tasked with informing FEE 202.

If the stability metric has not been satisfied, the assumed propagationdistance may be adjusted to update, e.g., in parallel, the tap weightsin FEE 202, iterative followed by another performance measure, etc.Conversely, if the stability metric has been met, an iterative LMS erroradaption may be enabled to adjust tap values in BEE 220 to obtainupdated BEE tap weights. In embodiments, system 300 may iteratively(e.g., linearly) sweep through a plurality of propagation distancesuntil the stability metric is satisfied. In embodiments, system 300 mayutilize a binary search, where the decisions directing the search areinformed by the sign of one or more tap weights obtained from BEE 220,e.g., after allowing time for convergence. If FEE 202 underestimates thepropagation distance, BEE 220 may increase compensation by settingcoefficients relatively high, for example, assuming three taps, BEE 220may set a relatively high positive value for the center tap and negativevalues for the second and third tap. Therefore, the sign of the centertap weight may be optionally used to steer selection of the tap weightsof FEE 202.

In embodiments, precomputing FEE 202 tap weights comprises aquantization step in which the nearest row in a lookup tablecorresponding to a distance shorter than the actual propagation distanceis used. For example, if a CD coefficient is precomputed in coarse stepsof, e.g., 0.5 km steps, starting at 0 km, the values in that row of thelookup table that are closest in propagation distance to the (initiallyunknown/assumed) distance that is shorter than true value should bechosen, in effect, selecting a mathematically rounded-up value(s),iteratively, until the stability metric satisfied. In embodiments, themagnitude and sign of the center tap of BEE 220 may be used as anindicator of the degree that the CD compensation in FEE 202 is too highor too low, e.g., combined with thresholds on the magnitudes of the tapweights of BEE 220 to determine whether the residual error is sufficientto warrant further updates to FEE 202. This indicator may then be usedto increment, decrement, or leave in place the currently selected row infront-end equalizer look-up table. In practice, the longest propagationdistance that still generates a positive sign for the center tap shouldbe chosen. The remaining, uncompensated CD may be absorbed by complexLMS BEE 220, e.g., along with any residual ISI. Once FEE 202 approachesthe true value of the propagation distance, BEE 220 can adjust to makesmaller corrections, e.g., by lowering the value for the center tap.

Conversely, if FEE 202 overestimates the propagation distance, BEE 220may compensate in the opposite direction, e.g., to undo anovercompensation, by reversing the signs of the taps. This methodeffectively splits CD correction duties between the taps of FEE 202 andtaps of adaptive BEE 220 and advantageously utilizes all available taps.Once updated BEE tap weights are obtained, they may be used to adjustthe tap weights in FEE 202, ultimately causing BEE 220 to output anequalized data bit stream that is substantially free from polarizationand phase control errors and is suitable for CD adaption error feedback.

In short, monitoring and adjusting tap values of FEE 202 enables BEE220, unlike FEE 202, to train itself. In embodiments, fixed tap valuesof FEE 202 may be updated as necessary, thereby, allowing a widetolerance in the otherwise fixed tap values of FEE 202, while achievingacceptable system performance.

The fact that the complex tap weights of analog BEE 220 continuouslyadapt, i.e., update, at a relatively slow rate, makes it cost-effectiveto observe them. Therefore, by observing taps at a rate significantlybelow the (e.g., 50 Gbaud) signal rate, advantageously, no digitalsolution is required, such that the effects of CD on high-speed opticalcommunication signals can be compensated or eliminated without the useof costly and power-hungry digitization by ADCs and subsequentprocessing by fast DSP hardware.

One additional advantage of using an approach that utilizes both FEE 202and BEE 220 is that BEE 220 may have a reduced number of complex andcostly analog taps, e.g., three instead of five taps, thus,significantly reducing system power and, in some applications, allowingBEE 220 to switch off once convergence has been assured in FEE 202 tofurther reduce power consumption.

FIG. 4A and FIG. 4B show simulation results for constellation diagramsfor X- and Y polarization output channels for a prior art equalizerdesign. FIG. 5A and FIG. 5B show improved simulation results forconstellation diagrams for X- and Y polarization output channels using aCD equalizer system according to embodiments of the present disclosure.It is noted that to make the simulations mathematically more convenient,linear algebra approaches were used to perform matrix multiplications togenerate simulation results 400-550. Since convolving two polynomialsresults in a large number of taps that may exceed the capacity, inembodiments, the problem may be treated as a frequency domain problem,and the tap weights of BEE 220 may be converted into a frequency domainresponse that may then be applied to FEE 202 in the frequency domain,for example, by treating the frequency response as that of a generalizedfilter that indicates where to adjust the gain.

FIG. 6 is a flowchart of an illustrative process for CD equalization,according to embodiments of the present disclosure. In embodiments, CDequalization process 600 begins at step 602 when an iterative LMS erroradaption is performed to adjust BEE tap weights. At step 604, the BEEtap weights may be used to adjust FEE tap weights. Finally, at step 606,the BEE may be used to output a data bit stream that has been equalized.It is noted that process steps disclosed herein may optionally beperformed. Steps may not be limited to the specific order set forthherein and may be performed in different orders or concurrently.

FIG. 7 is a flowchart of another illustrative process for CDequalization, according to embodiments of the present disclosure.Process 700 begins at step 702 when, a coarse CD compensation isperformed by applying to a receiver FEE tap weights that have beenprecomputed using an assumed propagation distance.

At step 704, e.g., after waiting a predetermined time after applying theFEE tap weights, it is determined whether the tap weights have caused adecision-directed tracking of channel phase and polarization rotationsto satisfy a stability metric.

At step 706, in response to the decision-directed tracking notsatisfying the stability metric, the assumed propagation distance may beadjusted to update the FEE tap weights.

Conversely, if the decision-directed tracking satisfies the stabilitymetric, an iterative LMS error adaption may be performed to adjust BEEtap weights to obtain updated BEE tap weights, at step 708.

At step 710, the updated BEE tap weights may be used to adjust FEE tapweights.

Finally, at step 712, the BEE may be used to output a data bit streamthat has been equalized.

Aspects of the present disclosure may be encoded upon one or morenon-transitory computer-readable media with instructions for one or moreprocessors or processing units to cause steps to be performed. It shallbe noted that the one or more non-transitory computer-readable mediashall include volatile and non-volatile memory. It shall be noted thatalternative implementations are possible, including a hardwareimplementation or a software/hardware implementation.Hardware-implemented functions may be realized using ApplicationSpecific Integrated Circuits (ASICs), programmable arrays, digitalsignal processing circuitry, or the like. Accordingly, the terms in anyclaims are intended to cover both software and hardware implementations.The term “computer-readable medium or media” as used herein includessoftware and/or hardware having a program of instructions embodiedthereon, or a combination thereof. With these implementationalternatives in mind, it is to be understood that the figures andaccompanying description provide the functional information one skilledin the art would require to write program code (i.e., software) and/orto fabricate circuits (i.e., hardware) to perform the processingrequired.

It shall be noted that embodiments of the present disclosure may furtherrelate to computer products with a non-transitory, tangiblecomputer-readable medium that have computer code thereon for performingvarious computer-implemented operations. The media and computer code maybe those specially designed and constructed for the purposes of thepresent disclosure, or they may be of the kind known or available tothose having skill in the relevant arts. Examples of tangiblecomputer-readable media include, but are not limited to: magnetic mediasuch as hard disks, floppy disks, and magnetic tape; optical media suchas CD-ROMs and holographic devices; magneto-optical media; and hardwaredevices that are specially configured to store or to store and executeprogram code, such as ASICs, programmable logic devices (PLDs), flashmemory devices, and ROM and RAM devices. Examples of computer codeinclude machine code, such as produced by a compiler, and filescontaining higher level code that are executed by a computer using aninterpreter. Embodiments of the present disclosure may be implemented inwhole or in part as machine-executable instructions that may be inprogram modules that are executed by a processing device. Examples ofprogram modules include libraries, programs, routines, objects,components, and data structures. In distributed computing environments,program modules may be physically located in settings that are local,remote, or both.

One skilled in the art will recognize no computing system or programminglanguage is critical to the practice of the present disclosure. Oneskilled in the art will also recognize that a number of the elementsdescribed above may be physically and/or functionally separated intosub-modules or combined together.

It will be appreciated to those skilled in the art that the precedingexamples and embodiments are exemplary and not limiting to the scope ofthe present disclosure. It is intended that all permutations,enhancements, equivalents, combinations, and improvements thereto thatare apparent to those skilled in the art upon a reading of thespecification and a study of the drawings are included within the truespirit and scope of the present disclosure. It shall also be noted thatelements of any claims may be arranged differently including havingmultiple dependencies, configurations, and combinations.

What is claimed is:
 1. A chromatic dispersion (CD) equalization systemcomprising: a Front-End Equalizer (FEE) comprising a set of FEE tapweights; and a Back-End Equalizer (BEE) comprising a set of BEE tapweights that are adjusted by an iterative least-mean-squared (LMS) erroradaption and made available to the FEE that uses the BEE tap weights toadjust the FEE tap weights, the BEE outputting a data bit stream thathas been equalized.
 2. The CD equalization system according to claim 1,wherein the FEE tap weights are static at a power-up condition when alink is established.
 3. The CD equalization system according to claim 1,wherein the iterative LMS error adaption uses an error slicer that hasbeen adapted for PAM or QAM modulation.
 4. The CD equalization systemaccording to claim 1, wherein the FEE, in response to receiving from theBEE CD adaption error feedback data that is substantially free frompolarization and phase control error, generates CD-equalized data. 5.The CD equalization system according to claim 1, wherein the iterativeLMS steps error adaption comprises a non-linear search of distancesuntil a residual inter-symbol interference (ISI) is reduced, theresidual ISI having been deduced once the BEE tap weights haveconverged.
 6. The CD equalization system according to claim 1, whereinthe iterative LMS error adaption is performed in response to determiningthat the FEE tap weights cause a decision-directed tracking of channelrotations to satisfy a stability metric.
 7. The CD equalization systemaccording to claim 6, wherein the stability metric comprises acorrelation between pairs of multiplicative coefficients used to performpolarization demixing.
 8. A chromatic dispersion (CD) equalizationmethod comprising: performing a coarse CD compensation by applying afirst set of tap weights to a receiver; performing iterative stepscomprising: in response to a decision-directed tracking not satisfying astability metric, performing steps comprising updating the first set oftap weights; and in response to the decision-directed trackingsatisfying the stability metric, performing a fine CD compensationcomprising: performing an iterative least-mean-squared (LMS) erroradaption to adjust a second set of tap weights to obtain updated tapweights; and using the updated tap weights to adjust the first set oftap weights; and outputting by the receiver a data bit stream that hasbeen equalized by a combination of the first set of tap weights and thesecond set of tap weights.
 9. The CD equalization method according toclaim 8, wherein the decision-directed tracking of channel rotationscomprises tracking of channel phase and polarization rotation.
 10. TheCD equalization method according to claim 8, wherein performing theiterative LMS error adaption comprises iteratively performing a gradientsearch.
 11. The CD equalization method according to claim 8, wherein thestability metric comprises a metric that indicates a degree of successof discerning separate constellation points.
 12. The CD equalizationmethod according to claim 11, wherein the stability metric comprises acorrelation between pairs of multiplicative coefficients used to performpolarization demixing.
 13. The CD equalization method according to claim11, wherein performing the iterative steps comprises sweeping through aplurality of distances until the stability metric is satisfied.
 14. TheCD equalization method according to claim 11, wherein performing theiterative steps comprises a non-linear search of distances until aresidual inter-symbol interference (ISI) is reduced, the residual ISIhaving been deduced once the second set of tap weights have converged.15. The CD equalization method according to claim 8, wherein adjustingthe updated tap weights comprises convolving the first set of tapweights with the second set of tap weights, the second set of tapweights being calculated by allowing an adaptive equalizer to converge.16. The CD equalization method according to claim 8, wherein the firstset of tap weights comprise precomputed values that have beenprecomputed before performing the iterative steps.
 17. The CDequalization method according to claim 16, further comprising, at astart-up condition, selecting from a lookup table a nearest row thatcorresponds to a propagation distance that is shorter than an actualpropagation distance, wherein selecting comprises incrementing thepropagation distance and observing magnitude and sign of a center tapafter an LMS error adaption.
 18. The CD equalization method according toclaim 17, wherein the LMS error adaption uses an error slicer that hasbeen adapted for PAM or QAM modulation.
 19. The CD equalization methodaccording to claim 8, further comprising, in response to receiving froma back-end equalizer CD adaption error feedback data that issubstantially free from polarization and phase control error, generatingCD-equalized data.
 20. The CD equalization method according to claim 8,wherein the first set of tap weights is static at a power-up conditionwhen a link is established.